Chi-Squared Test Calculator

This calculator uses the Pearson chi-squared test of independence applied to a 2 x N contingency table, where rows represent outcomes (converted, not converted) and columns represent variations. For each cell in the contingency table, the expected count under the null hypothesis of no association is: E_ij = (row_total_i * column_total_j) / grand_total The chi-squared statistic is: X^2 = sum of (O_ij - E_ij)^2 / E_ij Where O_ij is the observed count and E_ij is the expected count for each cell. The degrees of freedom for a 2 x N table is (2-1) * (N-1) = N-1, where N is the number of variations. The p-value is computed from the chi-squared CDF using the regularized incomplete gamma function. A p-value below 0.05 indicates that the observed differences in conversion rates are statistically significant at the 95% confidence level. Cramer's V is the effect size, computed as sqrt(X^2 / (n * min(r-1, c-1))). For a 2-row table, this simplifies to sqrt(X^2 / n). Values range from 0 (no association) to 1 (perfect association).